Efficient multifidelity data-informed models for urban air quality

这名学生将参与一个项目，该项目旨在解决目前影响人们健康的最重要的环境问题之一--城市空气污染--建模的挑战。虽然众所周知，城市空气质量可以用偏微分方程进行数学建模，但这类模型的不确定性传播需要具有许多不同输入的多个模型评估，如果只使用高保真模型，则会导致过多的计算需求。因此，迫切需要将这种技术与降阶方法和由观测数据集提供信息的参数估计相结合的模型。这个项目的目的是开发这样的多保真方法，通过结合数学建模、统计学、线性代数和数据科学的技术来加速不确定性传播的解决。该项目将把学生放在数值方法研究的前沿，并提供一个极好的机会来发展在应用数学、工程和工业之间工作的技能。

The student will be part of a project which addresses the challenge of modelling one of the most important environmental problems currently affecting people's health, urban air pollution. Although it is well established that urban air quality can be modelled mathematically using partial differential equations, the inclusion of uncertainty propagation for this class of models requires multiple model evaluations with many different inputs, leading to excessive computational demands if only a high-fidelity model is used. There is therefore a pressing need for models which combine such techniques with reduced order approaches and parameter estimation informed by observational data sets. The aim of this project is to develop such multifidelity methods to accelerate the solution of uncertainty propagation by combining techniques from mathematical modelling, statistics, linear algebra and data science. The project will place the student at the forefront of research in numerical methods, and provide an excellent opportunity to develop skills working at the interface between applied mathematics, engineering and industry.